Edge length display - disable exponential notation?
Alright... the cause of the problem is as asinine and unintuitive as it gets.

The scale of the Grid - even when it's not in use - affects the precision of any displayed measurment numbers. The relationship is inverse - the higher the scale, the less significant numbers you're shown.

Few examples -

Scale 10:



Scale 1:



Scale 0.1:



Brilliant.